1 citations · 2 across the 6 of their papers we have counts for
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Dynamical approximations of postsingularly finite entire maps
Malavika Mukundan, Nikolai Prochorov, Bernhard Reinke
We prove that every postsingularly finite entire map can be approximated by a sequence of postcritically finite complex polynomials such that their postsingular dynamic…
Iterated Monodromy Groups of Entire Maps and Dendroid Automata
Bernhard Reinke
This paper discusses iterated monodromy groups for transcendental functions. We show that for every post-singularly finite entire transcendental function, the iterated monodromy ac…
Parametric linearization of skew products
Pierre Berger, Bernhard Reinke
We establish a linearization criterion for skew products of contractions in any dimension. We prove their smooth or holomorphic parameter dependence. In the smooth setting, we use…
Diverging orbits for the Ehrlich-Aberth and the Weierstrass root finders
Bernhard Reinke
We show that the higher dimensional Weierstrass and Ehrlich-Aberth methods for finding roots of polynomials have infinite orbits that diverge to infinity. This is possible for the…
Iterated Monodromy Groups of Exponential Maps
Bernhard Reinke
This paper introduces iterated monodromy groups for transcendental functions and discusses them in the simplest setting, for post-singularly finite exponential functions. These gro…
The Weierstrass root finder is not generally convergent
Bernhard Reinke, Dierk Schleicher, Michael Stoll
Finding roots of univariate polynomials is one of the fundamental tasks of numerics, and there is still a wide gap between root finders that are well understood in theory and those…